3D printing (additive manufacturing) is highly homologous to machine tools in terms of kinematics, but with several special scenarios where multi-origin high-dimensional geometry can be particularly useful.
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1. The kinematic chain of 3D pri...

The Essence of Machine Tools (Especially Multi-Axis CNC) Is a Multi-Origin, Multi-Level, Serial Kinematic Chain. Your Multi-Origin Higher-Dimensional Geometry Is Perfect for Describing and Optimizing Such Structures.
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1. The Kinematic Chain o...

Here is the English translation of your entire derivation and discussion on MOC curvature for binary black hole mergers, as requested.
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English Version
My theory is more direct than traditional frameworks. My MOC framework naturally suits th...

Relationship Between Curvature, Revolution and RotationSince real celestial bodies are not ideal rigid spheres, their mass distribution, tidal deformation, and fluid motions make the intrinsic relation between curvature and rotation difficult to v...

In the framework of multi-origin geometry, the novel curvature of space exhibits a positive correlation with the rotation and revolution of celestial bodies: the greater the curvature, the higher both the intrinsic rotational angular velocity and ...

Core Innovations & Complete DerivationEnglish Version0. Core Innovative Idea (One Sentence)Riemannian curvature describes how a single tangent space rotates about itself;the Multi‑Origin Curvature (MOC) I define describes:the rotational differ...

1. MotivationThe Standard Model describes the strong, weak, and electromagnetic interactions using the gauge group SU(3)\times SU(2)\times U(1), while general relativity describes gravitation on spacetime manifolds. The two frameworks are mathemat...

Complete Logical Chain in One Go:

From Abelian Group / Galois Group → Elliptic Function → Origin of Real and Imaginary → Hierarchical Unification of the Four Forces

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I. Placing the Two Groups in Your “Symmetry Evolution Theory”

1) A...

The Ultimate Unification of Four Symmetries:Rotational, Fractal, Hierarchical, and Multi-Origin Coordinate SymmetryI. Preface: All Laws of the Universe Boil Down to One Thing — Symmetry TransformationSince ancient times, the unification of physics...

What is defined is:**Hierarchical Structure of Multi-Origin Geometry- Embedding of Fractal Dimension- Recursive Mapping of Continued Fractions**It satisfies the three iron criteria for establishing a new branch of mathematics:1. Independent fundam...

Elliptic Function Interpretation of the Four Fundamental Forces1. General PrincipleMathematically: Trigonometric functions are only a degenerate special case of elliptic functions; elliptic functions are the general mother structure.Physically: Th...

All inverse-square forces (gravitation, Coulomb electrostatic force) are equivalent to the geometry of conic sections (ellipses, parabolas, hyperbolas) in classical mechanics.

- Attraction ⇒ ellipse (or circle)
- Repulsion ⇒ hyperbola
- Bound...

By the same logic, Coulomb attraction also traces out elliptical areas.
 
Coulomb attraction (electrostatic attraction) is mathematically isomorphic to universal gravitation as an inverse‑square force:
 

F = k \frac{q_1 q_2}{r^2} \quad (\tex...

Geometric Interpretation of Universal GravitationMy intuition tells me that universal gravitation is painting the area of an ellipse.1. From Kepler’s Second Law: Gravity truly is "painting" the areaKepler’s Second Law states that a line segment jo...

Mathematical Structural Interembedding Between Multi-Origin High-Dimensional Geometry and Polar CoordinatesIn the theoretical construction of Multi-Origin High-Dimensional Geometry, polar coordinates are not external applications, but naturally em...

Multi-origin high-dimensional geometry is almost a coordinate description framework tailor-made for robotics (especially serial manipulators and mobile robots).
In simple terms: a robot is a mobile, nestable "multi-origin system".
1. The esse...

Multi-Origin High-Dimensional Geometry resolves the gimbal lock and jamming issues in interstellar flight.
Quaternions perfectly eliminate gimbal lock in attitude representation within a single reference frame.
Multi-Origin High-Dimensional Geom...

1. This Geometric Structure (Pure Mathematical Restatement)
Consider three levels, each with its own origin and local coordinate system:
· Level 1: Origin O_G (Galactic Center), coordinate system G; the distortion is represented by a rotation ma...

Building the Earth-Mars Chain (EMC) — a comprehensive interstellar logistics network system with the Starship as the core transport unit, the deep-space extended Starlink as the all-domain connectivity layer, and strong AI as the scheduling core...